Three-Dimensional Finite Element Analysis of Multiple-Grained Lead-Free Solder Interconnects

A combination of various experimental techniques was coupled with three-dimensional numerical simulation to study the strain distribution in anisotropic, heterogeneous lead (Pb)-free solder ball grid array interconnects used in electronic packages. An in situ full-field deformation map on the cross section of the joint showed a nonuniform strain distribution when the package was subjected to thermal loading. This nonuniformity was correlated with the locations of various grains on the cross section as obtained by orientation imaging microscopy (OIM) and optical microscopy. The solder interconnect was progressively sectioned and imaged under cross polarizers to discern the␣three-dimensional shapes of various grains in the solder interconnect. A methodology to replicate the three-dimensional shapes and orientations of the various grains and grain boundaries in a microstructure-based finite element model was developed. The numerical results were compared with the displacement and strain distributions obtained experimentally. The demonstrated strain localization along the grain boundaries in the case of multigrain joints and along the pad-solder interfaces in the case of the single-grain joints matched very well with the locations of plastic damage accumulation when the same interconnect was subjected to several thermal cycles.